Optical fibres are essential for many types of highly multiplexed and precision spectroscopy. The success of the new generation of multifibre instruments under construction to investigate fundamental problems in cosmology, such as the nature of dark energy, requires accurate modellization of the fibre system to achieve their signal-to-noise ratio (SNR) goals. Despite their simple construction, fibres exhibit unexpected behaviour including non-conservation of etendue (focal ratio degradation, FRD) and modal noise. Furthermore, new fibre geometries (non-circular or tapered) have become available to improve the scrambling properties that, together with modal noise, limit the achievable SNR in precision spectroscopy. These issues have often been addressed by extensive tests on candidate fibres and their terminations, but these are difficult and time-consuming. Modelling by ray tracing and wave analysis is possible with commercial software packages, but these do not address the more complex features, in particular FRD.
We use a phase-tracking ray-tracing method to provide a practical description of FRD derived from our previous experimental work on circular fibres and apply it to non-standard fibres. This allows the relationship between scrambling and FRD to be quantified for the first time. We find that scrambling primarily affects the shape of the near-field pattern but has negligible effect on the barycentre. FRD helps to homogenize the near-field pattern but does not make it completely uniform. Fibres with polygonal cross-section improve scrambling without amplifying the FRD. Elliptical fibres, in conjunction with tapering, may offer an efficient means of image slicing to improve the product of resolving power and throughput, but the result is sensitive to the details of illumination. We also investigated the performance of fibres close to the limiting numerical aperture since this may affect the uniformity of the SNR for some prime focus fibre instrumentation.